Question

South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $295,000 in the first year of operation to $1,080,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 20 42 69 98 175 2 101 141 149 211 288 3 168 250 333 388 436 4 6 20 47 91 181

Quarter	Year 1	Year 2	Year 3	Year 4	Year 5
1	20	42	69	98	175
2	101	141	149	211	288
3	168	250	333	388	436
4	6	20	47	91	181

Answer 1

b)

Value	Qtr1	Qtr2	Qtr3
20	1	0	0
101	0	1	0
168	0	0	1
6	0	0	0
42	1	0	0
141	0	1	0
250	0	0	1
20	0	0	0
69	1	0	0
149	0	1	0
333	0	0	1
47	0	0	0
98	1	0	0
211	0	1	0
388	0	0	1
91	0	0	0
175	1	0	0
288	0	1	0
436	0	0	1
181	0	0	0

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.810139
R Square	0.656325
Adjusted R Square	0.591886
Standard Error	79.7844
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	194503.4	64834.47	10.18521	0.000541
Residual	16	101848.8	6365.55
Total	19	296352.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	69	35.68067	1.93382	0.071025	-6.63964	144.6396
Qtr1	11.8	50.46008	0.233848	0.818069	-95.1706	118.7706
Qtr2	109	50.46008	2.160123	0.046281	2.029402	215.9706
Qtr3	246	50.46008	4.875141	0.000168	139.0294	352.9706

Estimated regression equation:  

ŷ = 69 + (12)Qtr1 + (109)Qtr2 + (246)Qtr3        

Quarter 1 forecast: x1 = 1, x2 = 0, x3 = 0  

ŷ = 69 + (12)*1 + (109)*0 + (246)*0 =    81

Quarter 2 forecast: x1 = 0, x2 = 1, x3 = 0  

ŷ = 69 + (12)*0 + (109)*1 + (246)*0 =    178

Quarter 3 forecast: x1 = 0, x2 = 0, x3 = 1  

ŷ = 69 + (12)*0 + (109)*0 + (246)*1 =    315

Quarter 4 forecast: x1 = 0, x2 = 0, x3 = 0  

ŷ = 69 + (12)*0 + (109)*0 + (246)*0 =    69

-----

c)

value	Period	Qtr1	Qtr2	Qtr3
20	1	1	0	0
101	2	0	1	0
168	3	0	0	1
6	4	0	0	0
42	5	1	0	0
141	6	0	1	0
250	7	0	0	1
20	8	0	0	0
69	9	1	0	0
149	10	0	1	0
333	11	0	0	1
47	12	0	0	0
98	13	1	0	0
211	14	0	1	0
388	15	0	0	1
91	16	0	0	0
175	17	1	0	0
288	18	0	1	0
436	19	0	0	1
181	20	0	0	0

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9810537
R Square	0.9624664
Adjusted R Square	0.9524574
Standard Error	27.231324
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	4	285229	71307.26	96.16039	1.671E-10
Residual	15	11123.18	741.545
Total	19	296352.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-73.875	17.75265	-4.16135	0.000836	-111.7139	-36.0361
Period	11.90625	1.076413	11.06105	1.31E-08	9.6119309	14.20057
Qtr1	47.51875	17.52273	2.711835	0.016073	10.169941	84.86756
Qtr2	132.8125	17.35663	7.651974	1.48E-06	95.817716	169.8073
Qtr3	257.90625	17.25621	14.94571	2.04E-10	221.12552	294.687

Estimated regression equation:  

ŷ = -74 + (48)Qtr1 + (133)Qtr2 + (258)Qtr3 + (12)Period  

Quarter 1 forecast: x1 = 1, x2 = 0, x3 = 0, t = 21  

ŷ = -74 + (48)*1 + (133)*0 + (258)*0 + (12)*21 =    224

Quarter 2 forecast: x1 = 0, x2 = 1, x3 = 0, t = 22  

ŷ = -74 + (48)*0 + (133)*1 + (258)*0 + (12)*22 =    321

Quarter 3 forecast: x1 = 0, x2 = 0, x3 = 1, t = 23  

ŷ = -74 + (48)*0 + (133)*0 + (258)*1 + (12)*23 =    458

Quarter 4 forecast: x1 = 0, x2 = 0, x3 = 0, t = 24  

ŷ = -74 + (48)*0 + (133)*0 + (258)*0 + (12)*24 =    212